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AN APPROACH TO THE DEFINITION OF COGNITIVE DEVELOPMENTAL STAGES IN SCHOOL MATHEMATICS
Author(s) -
HALFORD G. S.
Publication year - 1978
Publication title -
british journal of educational psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.557
H-Index - 95
eISSN - 2044-8279
pISSN - 0007-0998
DOI - 10.1111/j.2044-8279.1978.tb03016.x
Subject(s) - unary operation , cognition , task (project management) , function (biology) , binary number , cognitive development , psychology , binary relation , population , mathematics education , mathematical problem , sequence (biology) , computer science , cognitive psychology , mathematics , arithmetic , discrete mathematics , engineering , sociology , genetics , systems engineering , demography , neuroscience , evolutionary biology , biology
S ummary . Three levels of mathematical concepts are outlined. Level 1 consists of concepts which depend on binary relations and unary operations. Level 2 consists of concepts which can be encoded as binary operations, and Level 3 consists of concepts which can be expressed as compositions of binary operations. Three levels of cognitive development which correspond in theory to the levels of mathematical concept understanding are outlined, and appropriate illustrative performances are given. Samples of Australian and Canadian school children were tested on problems designed to require Level 2 or 3 mathematical understanding. Success rates were consistent with predictions for each age group. The application of cognitive development theory to the teaching of mathematics to children is considered, and an alternative approach is proposed. It is specifically predicted that ability to attain concepts at any of the three levels will be a function of information‐processing capacity, which will be a necessary but not sufficient condition. Once the minimum required information‐processing capacity is available, acquisition will be a function of experience and task variables. Thus concepts should be expected to emerge neither synchronously nor in any defined sequence, and they should emerge gradually rather than abruptly across an entire population.